Sequential Physics-Constrained Neural Operator Forward Modeling for the extit{Norne} Reservoir System

arXiv:2605.28909v1 Announce Type: new Abstract: We develop a comprehensive mathematical and computational framework for sequential surrogate modeling of three-phase black-oil reservoir dynamics using neural operators, with particular emphasis on Fourier Neural Operators (FNO) and their physics-informed variant (PINO). The application focus is the Norne benchmark reservoir, defined on a heterogeneous 46imes112imes22 grid (N=113,344 cells), with a production history spanning T=30 timesteps covering 3298 days. Our theoretical contributions are organized around four interlocking problems: (1) functional-analytic formulation in a product-Sobolev-space setting, including well-posedness of the implicit timestep map and sharp local Lipschitz estimates; (2) covariate shift quantification, proving that the Wasserstein-2 distance grows as W_2 leq arepsilon(L^n-1)/(L-1), with exponential population-risk discrepancy for L>1; (3) physics-constrained spectral stability, showing PINO training with lambda_R geq lambda^_R reduces the learned Jacobian spectral radius to rho_F + Clambda_R^{-1/2}, yielding uniform-in-time rollout error |elta_n| leq arepsilon/(1-rho); and (4) K-step TBPTT gradient analysis, deriving geometric bias decay O(rho^K), optimal window K^ = O(log(T/sigma^2)), and Adam convergence O(1/sqrt{t}) + O(rho^{K^}). Empirical validation confirms all theoretical predictions: autoregressive PINO surrogates sustain R^2>0.99 (oil), R^2>0.90 (gas), R^2approx 0.80 (pressure), and monotonically improving R^2 (water) across the full 3298-day horizon, trained on eight NVIDIA B200 GPUs in under one hour. A 1000-member ensemble runs in under one minute on a single B200 GPU, giving a {sim}10^4imes wall-clock speedup over the OPM finite-volume simulator.

Source: arXiv cs.LG | 2026-05-29